An ac source of angular frequency w is fed across a resistor r and a capacitor C in series. The current registered is I. If now the frequency of source is changed to w/3 (but maintaining the same voltage), the current in then circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency w [Roorkee 1996]

• A.            \[\sqrt{\frac{3}{5}}\]        
• B.            \[\sqrt{\frac{2}{5}}\]
• C.            \[\sqrt{\frac{1}{5}}\]        
• D.            \[\sqrt{\frac{4}{5}}\]